DLMF:4.37.E24 (Q1943): Difference between revisions

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Revision as of 19:17, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 19:17, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			principal branch of logarithm function
		Property / Symbols used: principal branch of logarithm function / rank
			Normal rank
		Property / Symbols used: principal branch of logarithm function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\ln\NVar{z}}}$ \ln@@{\NVar{z}}
		Property / Symbols used: principal branch of logarithm function / qualifier
			xml-id: C4.S2.E2.m2ahdec
		Property / Symbols used
			Q11244
		Property / Symbols used: Q11244 / rank
			Normal rank
		Property / Symbols used: Q11244 / qualifier
			Defining formula: ${\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}$ (\NVar{a},\NVar{b}]
		Property / Symbols used: Q11244 / qualifier
			xml-id: introduction.Sx4.p2.t1.r1.m3acdec
		Property / Symbols used
			Q10785
		Property / Symbols used: Q10785 / rank
			Normal rank
		Property / Symbols used: Q10785 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\setminus}}$ \setminus
		Property / Symbols used: Q10785 / qualifier
			xml-id: introduction.Sx4.p2.t1.r19.m2acdec
		Property / Symbols used
			Q10824
		Property / Symbols used: Q10824 / rank
			Normal rank
		Property / Symbols used: Q10824 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\cup}}$ \cup
		Property / Symbols used: Q10824 / qualifier
			xml-id: introduction.Sx4.p1.t1.r28.m2aadec
		Property / Symbols used
			Q11217
		Property / Symbols used: Q11217 / rank
			Normal rank
		Property / Symbols used: Q11217 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11217 / qualifier
			xml-id: C4.S1.XMD8.m1sdec

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Latest revision as of 19:17, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:4.37.E24	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\operatorname{arctanh}z=\tfrac{1}{2}\ln\left(\frac{1+z}{1-z}\right),}}$

0 references

DLMF id

DLMF:4.37.E24

0 references

constraint

${\displaystyle{\displaystyle z\in\mathbb{C}\setminus(-\infty,-1]\cup[1,\infty)}}$

0 references

Symbols used

Q11243

Defining formula

${\displaystyle{\displaystyle[\NVar{a},\NVar{b})}}$

xml-id

introduction.Sx4.p2.t1.r1.m4aadec

0 references

Q10923

Defining formula

${\displaystyle{\displaystyle\mathbb{C}}}$

xml-id

introduction.Sx4.p1.t1.r1.m2acdec

0 references

Q10784

Defining formula

${\displaystyle{\displaystyle\in}}$

xml-id

introduction.Sx4.p1.t1.r10.m2agdec

0 references

Q11248

Defining formula

${\displaystyle{\displaystyle\operatorname{arctanh}\NVar{z}}}$

xml-id

C4.S37.SS2.p1.m10acdec

0 references

principal branch of logarithm function

Defining formula

${\displaystyle{\displaystyle\ln\NVar{z}}}$

xml-id

C4.S2.E2.m2ahdec

0 references

Q11244

Defining formula

${\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}$

xml-id

introduction.Sx4.p2.t1.r1.m3acdec

0 references

Q10785

Defining formula

${\displaystyle{\displaystyle\setminus}}$

xml-id

introduction.Sx4.p2.t1.r19.m2acdec

0 references

Q10824

Defining formula

${\displaystyle{\displaystyle\cup}}$

xml-id

introduction.Sx4.p1.t1.r28.m2aadec

0 references

Q11217

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C4.S1.XMD8.m1sdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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